“finding a place for the mind in a world that is fundamentally physical”

—has been puzzled over for centuries, and is unlikely to be resolved any time soon. The reason is that apparently every possible solution has inadequacies. Anyone familiar with the philosophical literature is aware of all the problems with Cartesian substance dualism, reductive physicalism, eliminative materialism, behaviorism and functionalism, non-reductive physicalism and emergentism. One is tempted to agree with Colin McGinn that the cognitive apparatus of humans is intrinsically inadequate to the problem of explaining the relation between the mind and the brain. How something like consciousness can emerge from something like the brain seems totally inexplicable.

7 Answers
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The Mind-Body problem is based on a mistaken and non-empirical premise: that the world is “fundamentally physical.” Because every school of Buddhism that I’m aware of has avoided this error, it is hard to find any Buddhist explanations that address it in the terms of modern philosophy.

As I understand it, all the various theories you refer to stemmed from the basic project of trying to discern the mind of an inaccessible Creator through understanding his works (like we might try to understand a clockmaker’s mind by examining his clocks); and subsequently having to deal with the collapse of faith in such a Creator by trying to understand how the clocks could build and run themselves (so to speak).

This dead-end philosophizing has sustained itself not because of any advances in solving the problem created by this error; but by taking a free ride on the extraordinary scientific and technological advances that have been made without needing to question ontological assumptions. Yet it has left our society deeply impoverished in our knowledge and use of consciousness, which makes Buddhism a vital corrective for our modern age.

The one Buddhist teacher I know who has devoted significant attention to this issue is B. Alan Wallace. While embracing the scientific method, he is sharply critical of the kinds of philosophical baggage that shortcut applying this method to consciousness. To give a sense of his analysis, I’ll quote an extended passage from his chapter in an excellent book he edited, called “Buddhism & Science - Breaking New Ground” (pp 13-14), in which he addresses the 'physicalist' assumption of the dogma of scientific materialism:

The research instruments of science, since the time of Galileo, have been designed to measure physical phenomena only. Thus if other types of phenomena exist, they must lie outside the domain of science as it has developed thus far. Advocates of the metaphysical principle of physicalism, however, have concluded that only those phenomena that can be detected with the tools of science actually exist. The universe is believed to consist solely of matter and its emergent properties. To understand this principle, it is crucial to recognize that the matter in question is not the familiar stuff that we bump into in everyday experience. A rock held in the hand, for instance, is experienced as having a certain color, texture, and weight. But all those qualities are secondary attributes that exist, according to [sociobiologist Edward O.] Wilson, not in the objective world but as representations inside our heads. The matter that is the fundamental stuff of the objective universe, according to scientific materialism, exists independently of all such secondary attributes that arise only in relation to a conscious subject. The real properties of matter are its inherent primary attributes that exist independently of all modes of detection.

What does science know today about the nature of matter? Physicists agree that matter consists of atoms, which in turn are made up of elementary particles such as electrons and protons. There are then further speculations concerning quarks, superstrings, and so on with regard to the component parts of elementary particles. But the actual nature of these fundamental building blocks of the universe is somewhat shrouded in mystery. Some physicists argue that atoms are emergent properties of space or space-time. But which space are they referring to? There are actually countless possible spaces with their own geometries, each of which is equally valid and self-consistent. Others maintain that atoms are not things at all but are better viewed as sets of relationships (Wallace 1996:55).

Even if matter is regarded as some independent stuff existing independently in the objective universe, its mass and spatial and temporal dimensions are not fixed or absolute but, according to relativity theory, depend upon the inertial frame of reference from which they are measured. And, in terms of quantum mechanics, it appears increasingly dubious whether the elementary particles of matter have any discrete location independent of all systems of measurement. Ever since the origins of quantum mechanics experts have expressed diverse views, ranging from the assertion that elementary particles exist independently as real, distinct entities to the view that there is no objectively existing quantum realm at all (Herbert 1985)! As physics continues to progress, the primary status of matter appears to be on the decline. As physicist Steven Weinberg recently commented, “In the physicist’s recipe for the world, the list of ingredients no longer includes particles. Matter thus loses its central role in physics. All that is left are principles of symmetry” (Cole 1999).

Upon confronting such startling lack of consensus about the nature and primacy of matter, the physicalist may take refuge in the notion of energy and its conservation as the primary stuff of the universe. But, once again, one is bound for disappointment, for, according to physicist Richard Feynman, the conservation of energy is a mathematical principle, not a description of a mechanism or anything concrete. He then goes on to acknowledge, “It is important to realize that in physics today we have no knowledge of what energy is” (Feynman, Leighton, and Sands 1963:4–2).

For scientific materialists such as Edward Wilson, signs of the existence and primacy of matter are to be found everywhere, even though those signs are all indirect (existing, as they do, as mere mental representations). Although matter is never detected as an independently existent stuff in the objective world, it is assumed to be the origin and basis of all that we experience. As to its actual nature, there have always been many competing views, and the number of hypotheses does not appear to be on the decline. Upon reflection, it seems that matter presently fills the role for the materialist that God has traditionally filled for the theist. And the diverse speculative theories of “materialogians” provide little support for the belief that such mysterious stuff can support the ontological burden of the entire universe of subjective and objective phenomena.

I think the problem stems from a desire to know the mechanistic workings of reality; e.g. how one thing affects or effects another, rather than simple that it does so. Buddhism is, for the most part, terribly devoid of explanations about the former, since it is ultimately a practical path. As the Buddha said time and again,

Bhikkhus, both formerly and now what I teach is suffering and the cessation of suffering.

-- MN 22 (Bodhi, trans)

In the context of your question, as others have pointed out, there really isn't any problem on the surface: physical reality clearly exists, as does mental reality; they also clearly interact with each other in a manner that is fairly easily definable.

The problem comes when you try to know more beyond these simple facts, i.e. how and why they exist and interact the way they do. These questions are foreign to Buddhism because they are not really useful at all, and moreover are probably ultimately outside of the realm of what can be empirically known.

Namasthe Banthe -/\- Dhamma Greetings .In Madhupindika Sutta:( The Ball of Honey ) Some what clarification is given as "Dependent on eye & forms, eye-consciousness arises. The meeting of the three is contact. With contact as a requisite condition, there is feeling. What one feels, one perceives (labels in the mind). What one perceives, one thinks about. What one thinks about, one objectifies. Based on what a person objectifies, the perceptions & categories of objectification assail him/her with regard to past, present, & future forms cognizable via the eye. Re."Dhatu Vibhanga & Mula pariyaya"
– ShrawakaSep 2 '15 at 14:32

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@Shrawaka that passage is descriptive, not explanatory; it doesn't answer the question of how mind and body are able to interact, just describes the manner in which they do.
– yuttadhammoSep 2 '15 at 14:35

The relationship between body and mind is well described by the Buddha in form of e.g. the 5 aggregates i.e., materiality, feeling, perception, mental formations, consciousness and Dependent Origination.

But not only is it well described, the Buddha teaches us to go and find out for ourselves through the practice of insight meditation.

Philosophy and science fails the perspective by both holding an extreme view.

Philosophy is only based on intellectual knowledge, i.e. knowledge without any reference point (experiental knowledge) to reality.

Science holds the annihilationist-view and believes that the Mind/Consciousness is created by the brain and that when the physical body breaks down then the Mind will also "die".

One answer is that reality is neither primarily physical nor mind, but awareness. Looking at Physics, we see the two-slit experiment, which seems to indicate that objects such as photons are "aware" of their environment and "make choices".

So, the simplest answer is to remove the quotes. Every thing, down to the lowest level of being, has awareness, and makes choices. Done.

In Dhatu-vibhanga Sutta: An Analysis of the Properties "'A person has six properties.' Thus was it said. In reference to what was it said? These are the six properties: the earth property, the liquid property, the fire property, the wind property, the space property, the consciousness property. 'A person has six properties.' Thus was it said, and in reference to this was it said. accesstoinsight.org/tipitaka/mn/mn.140.than.html
– ShrawakaSep 2 '15 at 13:51

The evidence or proof your looking for won't come by using intellectual concepts or material tools. The mind-body relationship happens at extremly fast speeds, in the labratory of one's moment by moment experience, something like this: Eye consciousness(mind) makes contact with a rose that causes desire to have the rose(mind). That causes the arm to go reaching out(body) to pick the rose. Accidently a thorn pricks the finger causing a pain signal to go to the brain(body) causing a negative reaction to the pain(mind) causing the arm to move away from the threat(body) and so on. I hope this helps. -Metta

In The Root of All Things “He perceives the base of infinite consciousness as the base of infinite consciousness. Having perceived the base of infinite consciousness as the base of infinite consciousness, he conceives himself as the base of infinite consciousness, he conceives himself in the base of infinite consciousness, he conceives himself apart from the base of infinite consciousness, he conceives the base of infinite consciousness to be ‘mine,’ he delights in the base of infinite consciousness. Why is that? Because he has not fully understood it, I say. suttacentral.net/en/mn1
– ShrawakaSep 2 '15 at 14:04

Yes, the mind-body problem is NOT a problem - it an interaction between the mind and the body. I do agree with earlier yuttadhammo's comments and with the other similar comments.
The mind and the body influence one another in one or another way. Mostly the mind governs the body.
There are mounting evidence of how the mind affect the body. If you have a look the outcomes of implication of mindfulness practices/meditation in psychotherapy you will be convinced. You will find that even a few meditation sessions enhance people's well-being. These outcomes of mindfulness meditations say that the mind reduces symptoms of psychopathologies such as stress and depression levels. You may ask what is about? From perspective of biological psychology and body physiology, it says that by meditating you training your mind ( about your feeling, cognition and emotion), which in turn influence your neurons and endocrine system to decrease or increase particular neurotransmitters, and of course taking, controlling neuron firing. This is the final outcome that we can measure in numbers. Don't we? In is not introspective evidence, not subjective it is measurable biochemical stuff in your in my body.
Bringing these together it become clear that the mind governs the body in one or another way. That mean they interact with each other. In other words, by training your mind (mindfulness meditation) you influencing your body through through emotion regulation, feeling and cognition (letting go, accepting thing you can not control and so on). These changes in turn in one or another way affect you body physiology (hormones, neurotransmitters..). And the final outcome are reduced ill health symptoms and enhanced well-being.

The mind body relationships is well explained in the Patthana. This is a wast and complex subject but let me highlight some of them.

Let's take the one of the relationships Ārammaṇa paccaya – object condition. Here combination of object (89 cittas, 52 cetasikas, 28 rūpas, Nibbāna, Paññatti) lead to mind (89 cittas, 52 cetasikas). This is just one such instance. For further information see: Paṭṭhāna - conditional relations part 1part 2 by Ayya Agganyani which is a good summary (but as of now still incomplete) and other literature on Paṭṭhāna - Conditional Relations perhaps from http://www.abhidhamma.com/.

The relationships include:

body conditioning mind, body, mind and body

mind conditioning mind, body, mind and body

mind and body conditioning mind, body, mind and body

Though I have taken liberty to condense the multiple relationships a summarization of the Paṭṭhāna by Dr. Nandamālābhivaṃsa contains this in more detail from page 7 onwards.